# How to calcuate forward exchange rate or interest rate parity?

Suppose USD/SGD 1.35-1.39 bid and ask. Given the bank quoted interest rate on USD is 1.96% - 2.083% pa and interest rate on SGD is 3.5% - 3.656% pa. How to calculate the forward bid and ask exchange rate for USD/SGD?

Wikipedia gives

``````Forward Rate = Spot Rate X [(1 + if) / (1 + id)]
``````

But given the above scenario, it doesn't say which rate to use for spot rate, if and id.

Also when I read some book, the formula is given as

``````Forward Rate = Spot Rate X [(1 + i_price) / (1 + i_base)]
``````

So which is correct, since price-foreign and base-domestic relationship is not always consistent in currency pair quotations?

Investopedia says

The first currency of a currency pair is called the "base currency", and the second currency is called the "quote currency".

Wikipedia says

id is the interest rate in domestic currency (base currency); if is the interest rate in foreign currency (quoted currency)

Furthermore, Investopedia says about Direct Quote

A foreign exchange rate quoted as the domestic currency per unit of the foreign currency.

What exactly is "domestic" and "foreign"? Seems like they like to swing things around and around?

Base Currency

When expressed in plain English, an exchange rate is conveyed using a sentence "One USD can be converted to 1.3579 SGD", or "1.3579 SGD can buy One USD". The currency after the word "One" is always called the "Base Currency". (USD is the Base Currency in those sentences).

Currency Pair Interpretation

In the forex market, a currency pair can be written in the form of USD/SGD, USD.SGD, USD:SGD, or even USDSGD. They all mean "1 USD = ? SGD" and the first currency (USD) is the Base Currency (because it is after "1").

If you switch the pair around, SGD/USD would mean "1 SGD = ? USD", in which SGD is the Base Currency.

Textbook conventions are reversed

Every textbook I've read, including High School and College Textbooks in the US, Chartered Financial Analyst materials, and some Wikipedia pages writes pairs in the completely opposite way. USD/SGD in textbook means "? USD per 1 SGD", while in the forex market, USD/SGD means "1 USD to ? SGD".

In textbooks, a slash "/" means per (due to conventions in high school maths), while in the forex market, a slash (or other symbol) means to.

In other words, without additional information, you cannot tell if USD/SGD has USD as Base or SGD as Base.

For the remaining part below, assume the Forex convention, ignore the textbook convention. i.e. the first Currency is always the Base

Direct vs Indirect Quote

For each pair, there is a more popular way to quote. For example, everybody in the Forex market only quotes USD/SGD. Nobody quotes SGD/USD. Same the EUR/USD, nobody quotes USD/EUR.

The retail banking FX is different. Local banks publishes Direct Quotes. It means that "Foreign Currency is always Base Currency", i.e. How much SGD (Local) does it cost to buy One USD (Foreign = Base). So if banks in Singapore says "Rate of EUR is 1.4962, Rate for MYR is 0.35657", it means "EUR/SGD is 1.4962, MYR/SGD is 0.35657".

Formula for Futures

Remember this fact: For Country A and Country B, if country A has lower interest rate than country B, Country A's currency is expected to "appreciate".

Another fact: An increase in an exchange rate (forex market convention) means a appreciation in of Base Currency. So if USD/CAD increases, it means that USD appreciates, because USD is the base.

Forward Rate = Spot Rate x [(1 + Interest_A) / (1 + Interest_B)]

So if the Forward Rate and Spot Rate are in the the forex market convention (and not textbook convention), and the pair is USD/CAD, USD interest rate is 0.25% and CAD interest rate is 0.75%, you can infer that Forward Rate for USD/CAD should be higher than Spot Rate because USD has lower interest rate. So Interest_A is 0.75% and Interest_B is 0.25%.

So the correct formula for the forex market is

It is meaningless to remember formulas in the form of "Domestic" and "Foreign", because you could be living in Singapore and trading EUR/USD.

Only use interest rate from Central banks and Exchange Rates from brokers

This means you do not use the interest rate quoted by retail bank. Brokers can give FX quotes in 0.02% spread. Midpoint of a huge retail spread does not work.

Confirm with real futures quotes

Look at http://www.cmegroup.com/market-data/delayed-quotes/fx.html to see actual futures price to confirm if your formula works. Note that almost every pair for CME Futures has "Foreign as Base". "Canadian Dollar Futures" represents CAD/USD instead of the more popular USD/CAD.

• Very complete answer. I'll add that forex markets often display EURUSD to mean long EUR and short USD and you rarely see EUR/USD. As most would read that as EUR per one USD as you mentioned. Though I have seen EUR/USD used both ways before even in the same text! – rhaskett Jul 13 '15 at 22:55
• Another confusion is sometimes instead of "appreciate" or "depreciate" and "depreciated", they will write in English, for example when talking about USD/EUR = 4.0234, "EUR is expected to rise (fall)." In this case, how would you interpret what is "EUR rising" between USD and EUR? – Jake Aug 1 '15 at 6:47

Nope nobody is swinging things around, you are confusing yourself. Both formulas are correct but they are confusing you with the terminology.

`id` is the same as `i_base` under the assumption that you will use domestic currency as your base currency.

`if` is the same as `i_price` under the assumption that you will use foreign currency as the currency in the numerator.

And example is `Spot rate` is 1.35, `if` is 1.96% and `id` is 3.5%. This is considering you are using SGD as your base currency. If you want the other way, inverse your spot rate and use the interest rates appropriately.

A foreign exchange rate quoted as the domestic currency per unit of the foreign currency.

If your domestic currency is `SGD` and you want it in terms of `USD`, means how many `SGD` you will receive per `1 USD`. You can replace `USD` for any other currency you want, which you want to convert to your `SGD` to.

• How about the part about calculating the forward rate? Does the formula care about whether it is direct or indirect quote? Because `id` and `if` is not always the same as `ibase` and `iprice`. So what is the correct formula? – Jake Jul 10 '15 at 16:13
• @Jake Can you confirm if you read the formula for FX in your book ? And what does the book define as `i_price` ? I am assuming you are reading formulas for different instruments. – DumbCoder Jul 10 '15 at 16:18
• The book I am reading does not say price or base; or domestic or foreign; it's just using currency symbols but each time it is consistently using price interest rate divided by base interest rate in its examples. It does not mention direct or indirect quote. – Jake Jul 10 '15 at 16:30
• Anyhow, without relying on other sources, can you confidently point out what is the correct formula based on your knowledge? Thanks a lot for your help. – Jake Jul 10 '15 at 16:32